Part I (a) Find the transfer function description associated with the following difference equation. This difference equation could be associated with the dynamics of a servo motor that has been sampled to produce a discrete-time difference equation. g[n] — 1.905g[n — 1] + 0.90489[n – 2] = 0.04837u[n — 1] + 0.04679u[n — 2]- (b) Find the poles and zeroes of the transfer function found in part (a) and comment on the stability of this open-loop system. Part II Suppose constant output feedback is applied to the system in Part I. That is let U (2) = R(z) - Y(z), where R(z) is a reference input that will be applied to the closed-loop system. (a) Find the transfer function between the reference input, R(z), and the output signal, Y (2). (b) Find the poles and zeroes of this closed-loop transfer function and comment on the stability of the closed-loop system. Part III Derive a state space representation for the difference equation in Part II. Notice that this difference equation also contains delays in the input terms. Even with the delays in the input terms, the state space representation is still only second order. Thus, if one draws a block diagram representation with the smallest number of delay blocks, then the block diagram will only contain two delay blocks.

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